What does rms mean for a sinusoidal AC voltage?

State the relationship between angular frequency \(\omega\) and frequency \(f\).

A sinusoidal voltage has peak value \(170\,\mathrm V\). Find its rms value.

An AC signal has frequency \(60\,\mathrm{Hz}\). Find its angular frequency.

A sinusoidal current has \(I_{\mathrm{rms}}=3.0\,\mathrm A\). Find its peak current.

A voltage is \(v(t)=80\cos(100\pi t)\,\mathrm V\). Find the peak voltage, rms voltage, angular frequency, frequency, and period.

Voltage is \(v(t)=V_0\cos(\omega t+30^\circ)\) and current is \(i(t)=I_0\cos(\omega t-10^\circ)\). What is the phase difference, and which signal leads?

A sinusoidal voltage is \(120\,\mathrm V\) rms at \(50\,\mathrm{Hz}\) with zero phase. Write \(v(t)\) using cosine form.

Show that the rms value of \(V_0\cos\omega t\) is \(V_0/\sqrt2\).

Two sinusoidal voltages of the same frequency have rms values \(30\,\mathrm V\) and \(40\,\mathrm V\), with a \(90^\circ\) phase difference. Find the rms value of their phasor sum.